plotCSedges.tri {pcds.ugraph}

The plot of the edges of the underlying or reflexivity graphs of the Central Similarity Proximity Catch Digraph (CS-PCD) for 2D data - one triangle case

Description

Plots the edges of the underlying or reflexivity graphs of the Central Similarity Proximity Catch Digraph (CS-PCD) whose vertices are the data points, Xp and the triangle tri. CS proximity regions are constructed with respect to the triangle tri with expansion parameter t > 0, i.e., edges may exist only for Xp points inside the triangle tri.

Edge regions are based on center M=(m_1,m_2) in Cartesian coordinates or M=(\alpha,\beta,\gamma) in barycentric coordinates in the interior of the triangle tri; default is M=(1,1,1), i.e., the center of mass of tri. With any interior center M, the edge regions are constructed using the extensions of the lines combining vertices with M.

See also (Ceyhan (2005, 2016)).

Usage

plotCSedges.tri(
  Xp,
  tri,
  t,
  M = c(1, 1, 1),
  ugraph = c("underlying", "reflexivity"),
  asp = NA,
  main = NULL,
  xlab = NULL,
  ylab = NULL,
  xlim = NULL,
  ylim = NULL,
  edge.reg = FALSE,
  ...
)

Arguments

Xp

A set of 2D points which constitute the vertices of the underlying or reflexivity graphs of the CS-PCD.

tri

A 3 \times 2 matrix with each row representing a vertex of the triangle.

t

A positive real number which serves as the expansion parameter in CS proximity region.

M

A 2D point in Cartesian coordinates or a 3D point in barycentric coordinates which serves as a center in the interior of the triangle tri; default is M=(1,1,1), i.e., the center of mass of tri.

ugraph

The type of the graph based on CS-PCDs, "underlying" is for the underlying graph, and "reflexivity" is for the reflexivity graph (default is "underlying").

asp

A numeric value, giving the aspect ratio y/x (default is NA), see the official help page for asp by typing "? asp".

main

An overall title for the plot (default=NULL).

xlab, ylab

Titles for the x and y axes, respectively (default=NULL for both).

xlim, ylim

Two numeric vectors of length 2, giving the x- and y-coordinate ranges (default=NULL for both).

edge.reg

A logical argument to add edge regions to the plot, default is edge.reg=FALSE.

...

Additional plot parameters.

Value

A plot of the edges of the underlying or reflexivity graphs of the CS-PCD whose vertices are the points in data set Xp and the triangle tri

Author(s)

Elvan Ceyhan

References

Ceyhan E (2005). An Investigation of Proximity Catch Digraphs in Delaunay Tessellations, also available as technical monograph titled Proximity Catch Digraphs: Auxiliary Tools, Properties, and Applications. Ph.D. thesis, The Johns Hopkins University, Baltimore, MD, 21218.

Ceyhan E (2016). “Edge Density of New Graph Types Based on a Random Digraph Family.” Statistical Methodology, 33, 31-54.

See Also

plotCSedges, plotASedges.tri, plotPEedges.tri, and plotCSarcs.tri

Examples

#\donttest{
A<-c(1,1); B<-c(2,0); C<-c(1.5,2);
Tr<-rbind(A,B,C);
n<-10

set.seed(1)
Xp<-pcds::runif.tri(n,Tr)$g

M<-as.numeric(pcds::runif.tri(1,Tr)$g)
t<-1.5
plotCSedges.tri(Xp,Tr,t,M,edge.reg = TRUE,xlab="",ylab="")
plotCSedges.tri(Xp,Tr,t,M,ugraph="r",edge.reg = TRUE,xlab="",ylab="")

#can add vertex labels and text to the figure (with edge regions)
Ds<-pcds::prj.cent2edges(Tr,M); cent.name="M"

txt<-rbind(Tr,M,Ds)
xc<-txt[,1]+c(-.02,.02,.02,.02,.04,-0.03,-.01)
yc<-txt[,2]+c(.02,.02,.02,.07,.02,.04,-.06)
txt.str<-c("A","B","C",cent.name,"D1","D2","D3")
text(xc,yc,txt.str)
#}